Asymptotic analysis for interactive oscillators of the van der Pol type

We consider the N-oscillator system of the van der Pol type, which contains a small positive parameter . multiplying the non-linear damping and the random disturbance. For a formulation of the output we take the solution X(t) = (Xi(t))i=1···,N of the system of 2N-dimensional stochastic differential equations. Rotating each component Xi(t) about the origin of the plane by an angle t, we find that on time scales of order 1/. together with sufficiently large N each Xi(t) behaves as the equi-ultimately bounded solution of an equation of the McKean type admitting a stationary probability distribution.